Problem: If $x \barwedge y = x+3y$ and $x \triangleleft y = x^{2}-3y^{2}$, find $(-6 \triangleleft -5) \barwedge 2$.
Answer: First, find $-6 \triangleleft -5$ $ -6 \triangleleft -5 = (-6)^{2}-3(-5)^{2}$ $ \hphantom{-6 \triangleleft -5} = -39$ Now, find $-39 \barwedge 2$ $ -39 \barwedge 2 = -39+(3)(2)$ $ \hphantom{-39 \barwedge 2} = -33$.